Finite Group Databasebeta

← C2×#13072609 #14921295

Subgroups — C2×#13072609 #14921295

Order 2816.

3958 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66999C211yesmaximal, characteristic, complemented
2C22×#66946C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
4#13072609C2116yesmaximal, direct product factor
5C2×#10622604C211yesmaximal, characteristic, complemented
6C2×#10622574C211yesmaximal, characteristic, complemented
7C2×#10622844C211yesmaximal, characteristic, complemented
8C2×#10622573C211yesmaximal, characteristic
9C2×#10622603C211yesmaximal, characteristic, complemented
10C2×#10622557C211yesmaximal, characteristic, complemented
11C2×#10622594C211yesmaximal, characteristic, complemented
12C2×#10622591C211yesmaximal, characteristic, complemented
13C2×#10622826C211yesmaximal, characteristic, complemented
14C2×#10622569C211yesmaximal, characteristic, complemented
15C2×#10622602C211yesmaximal, characteristic, complemented
16C22×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
17C23×Q8×C11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C23×D44C2211yescharacteristic
22C23×C4×D11C2211yescharacteristic
23C23×C4×D11C2211yescharacteristic
24C2×C11×C22⋊Q8—28no—
25C2×C11×C22⋊Q8C2218yescomplemented
26C22×C11×C4⋊C4C2211yescharacteristic
27C22×C11×C4⋊C4C2211yescharacteristic
28C22×C11×C4⋊C4C2211yescharacteristic
29C22×C11×C22⋊C4C2211yescharacteristic
30C22×C11×C22⋊C4C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic
33C2×#66999—28no—
34C2×#66999C2218yescomplemented
35C2×C4×C22⋊D11—28no—
36C2×C4×C22⋊D11C2218yescomplemented
37C22×(C2×D11)⋊C4C2211yescharacteristic
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C22×(C2×D11)⋊C4C2211yescharacteristic
40C22×(C2×D11)⋊C4C2211yescharacteristic
41C22×(C2×D11)⋊C4C2211yescharacteristic
42C22×(C2×D11)⋊C4C2211yescharacteristic
43C22×(C2×D11)⋊C4C2211yescharacteristic
44C22×(C2×D11)⋊C4C2211yescharacteristic
45C22×C4⋊Dic11C2211yescharacteristic
46C22×Dic11⋊C4C2211yescharacteristic
47C22×Dic11⋊C4C2211yescharacteristic
48C22×C4×Dic11C2211yescharacteristic
49C22×C4×Dic11C2211yescharacteristic
50C2×#66946—28no—
51C2×#66946C2218yescomplemented
52#10622844C2218yescomplemented
53#10622826C2218yescomplemented
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61C2×C11⋊#95C2211yescharacteristic
62#10622604C2218yescomplemented
63#10622603C2218yescomplemented
64#10622602C2218yescomplemented
65#10622594C2218yescomplemented
66#10622591C2218yescomplemented
67#10622574C2218yescomplemented
68#10622573C2218yes—
69#10622569C2218yescomplemented
70#10622557C2218yescomplemented
71C25×C11C2311yescharacteristic
72C24×D11C2311yescharacteristic
73C24×D11C2311yescharacteristic
74C22×Q8×C11—24no—
75C22×Q8×C11—24no—
76C22×Q8×C11—42no—
77C22×Q8×C11C2314yes—
78C23×C4×C11—24no—
79C23×C4×C11—24no—
80C23×C4×C11—42no—
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2314yes—
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C22×C22⋊D11—24no—
89C22×C22⋊D11—24no—
90C22×C22⋊D11—24no—
91C22×C22⋊D11—24no—
92C22×C22⋊D11—24no—
93C22×C22⋊D11—42no—
94C22×C22⋊D11C2314yes—
95C22×C22⋊D11C2314yes—
96C23×Dic11C2311yescharacteristic
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2311yescharacteristic
100C23×Dic11C2311yescharacteristic
101C23×Dic11C2311yescharacteristic
102C22×D44—24no—
103C22×D44—24no—
104C22×D44—24no—
105C22×D44C2314yes—
106C22×C4×D11—24no—
107C22×C4×D11—24no—
108C22×C4×D11—24no—
109C22×C4×D11—24no—
110C22×C4×D11—42no—
111C22×C4×D11—42no—
112C22×C4×D11C2314yes—
113C22×C4×D11C2314yes—
114C11×C22⋊Q8—232no—
115C2×C11×C4⋊C4—24no—
116C2×C11×C4⋊C4—24no—
117C2×C11×C4⋊C4D418yescomplemented
118C2×C11×C4⋊C4C2314yes—
119C2×C11×C4⋊C4C2314yes—
120C2×C11×C4⋊C4C2314yes—
121C2×C11×C22⋊C4—24no—
122C2×C11×C22⋊C4—24no—
123C2×C11×C22⋊C4C2314yes—
124C2×C11×C22⋊C4C2314yes—
125C2×C22⋊Dic11—24no—
126C2×C22⋊Dic11—24no—
127C2×C22⋊Dic11C2314yes—
128C2×C22⋊Dic11C2314yes—
129#66999—232no—
130C4×C22⋊D11—232no—
131C2×(C2×D11)⋊C4—24no—
132C2×(C2×D11)⋊C4—24no—
133C2×(C2×D11)⋊C4—24no—
134C2×(C2×D11)⋊C4—24no—
135C2×(C2×D11)⋊C4—24no—
136C2×(C2×D11)⋊C4—24no—
137C2×(C2×D11)⋊C4—24no—
138C2×(C2×D11)⋊C4—42no—
139C2×(C2×D11)⋊C4C2314yes—
140C2×(C2×D11)⋊C4C2314yes—
141C2×(C2×D11)⋊C4C2314yes—
142C2×(C2×D11)⋊C4C2314yes—
143C2×(C2×D11)⋊C4C2314yes—
144C2×(C2×D11)⋊C4C2314yes—
145C2×(C2×D11)⋊C4C2314yes—
146C2×(C2×D11)⋊C4C2314yes—
147C2×C4⋊Dic11—24no—
148C2×C4⋊Dic11C2314yes—
149C2×Dic11⋊C4—24no—
150C2×Dic11⋊C4D418yescomplemented
151C2×Dic11⋊C4C2314yes—
152C2×Dic11⋊C4C2314yes—
153C2×C4×Dic11—24no—
154C2×C4×Dic11—24no—
155C2×C4×Dic11C2314yes—
156C2×C4×Dic11C2314yes—
157#66946—232no—
158C11⋊#95C2314yes—
159C11⋊#95C2314yes—
160C11⋊#95C2314yes—
161C11⋊#95C2314yes—
162C11⋊#95C2314yes—
163C11⋊#95C2314yes—
164C11⋊#95C2314yes—
165C11⋊#95C2314yes—
166C2×#2463—111nomaximal, Sylow
167C24×C11—22no—
168C24×C11—22no—
169C24×C11—22no—
170C24×C11—22no—
171C24×C11—22no—
172C24×C11—22no—
173C24×C11#4114yes—
174C24×C11C2412yes—
175C24×C11C2411yescharacteristic
176C23×D11—22no—
177C23×D11—22no—
178C23×D11—22no—
179C23×D11—22no—
180C23×D11—22no—
181C23×D11—22no—
182C23×D11—22no—
183C23×D11—22no—
184C23×D11—22no—
185C23×D11—22no—
186C23×D11—22no—
187C23×D11—22no—
188C23×D11#4114yes—
189C23×D11#4114yes—
190C23×D11C2412yes—
191C23×D11C2412yes—
192C2×Q8×C11—28no—
193C2×Q8×C11—28no—
194C2×Q8×C11—44no—
195C2×Q8×C11—416no—
196C22×C4×C11—22no—
197C22×C4×C11—22no—
198C22×C4×C11—22no—
199C22×C4×C11—22no—
200C22×C4×C11—22no—
201C22×C4×C11—22no—
202C22×C4×C11—22no—
203C22×C4×C11—22no—
204C22×C4×C11—22no—
205C22×C4×C11—22no—
206C22×C4×C11—22no—
207C22×C4×C11—22no—
208C22×C4×C11—22no—
209C22×C4×C11—22no—
210C22×C4×C11—28no—
211C22×C4×C11—28no—
212C22×C4×C11—44no—
213C22×C4×C11—416no—
214C22×C4×C11C2×D414yes—
215C22×C4×C11C2×D414yes—
216C22×C4×C11C2×D414yes—
217C22×C4×C11C2×D414yes—
218C22×C4×C11C2412yes—
219C22×C4×C11C2412yes—
220C22×C4×C11C2412yes—
221C22×C4×C11C2412yes—
222C22×C4×C11C2412yes—
223C22×C4×C11C2412yes—
224C2×C22⋊D11—232no—
225C2×C22⋊D11—28no—
226C2×C22⋊D11—28no—
227C2×C22⋊D11—28no—
228C2×C22⋊D11—28no—
229C2×C22⋊D11—28no—
230C2×C22⋊D11—44no—
231C2×C22⋊D11—416no—
232C22×Dic11—22no—
233C22×Dic11—22no—
234C22×Dic11—22no—
235C22×Dic11—22no—
236C22×Dic11—22no—
237C22×Dic11—22no—
238C22×Dic11—22no—
239C22×Dic11—22no—
240C22×Dic11—22no—
241C22×Dic11—22no—
242C22×Dic11—22no—
243C22×Dic11—22no—
244C22×Dic11—22no—
245C22×Dic11—22no—
246C22×Dic11—22no—
247C22×Dic11—22no—
248C22×Dic11C2×D414yes—
249C22×Dic11C2×D414yes—
250C22×Dic11C2412yes—
251C22×Dic11C2412yes—
252C22×Dic11C2412yes—
253C22×Dic11C2412yes—
254C22×Dic11C2412yes—
255C22×Dic11C2412yes—
256C2×D44—232no—
257C2×D44—28no—
258C2×D44—28no—
259C2×D44—28no—
260C2×C4×D11—28no—
261C2×C4×D11—28no—
262C2×C4×D11—28no—
263C2×C4×D11—28no—
264C2×C4×D11—44no—
265C2×C4×D11—44no—
266C2×C4×D11—416no—
267C2×C4×D11—416no—
268C11×C4⋊C4—28no—
269C11×C4⋊C4—28no—
270C11×C4⋊C4C2×D4116yescomplemented
271C11×C22⋊C4—28no—
272C11×C22⋊C4—28no—
273C22⋊Dic11—28no—
274C22⋊Dic11—28no—
275(C2×D11)⋊C4—28no—
276(C2×D11)⋊C4—28no—
277(C2×D11)⋊C4—28no—
278(C2×D11)⋊C4—28no—
279(C2×D11)⋊C4—28no—
280(C2×D11)⋊C4—28no—
281(C2×D11)⋊C4—28no—
282(C2×D11)⋊C4—44no—
283C4⋊Dic11—28no—
284Dic11⋊C4—28no—
285Dic11⋊C4C2×D4116yescomplemented
286C4×Dic11—28no—
287C4×Dic11—28no—
288C22×C22⋊Q8—111no—
289C22×C22⋊Q8D1111yescharacteristic, complemented
290C22×C4×D4—111no—
291C22×C4×D4—111no—
292#2463—1116no—
293C2×#394—111no—
294C2×#394—111no—
295C2×#393—111no—
296C2×#392—111no—
297C2×#388—111no—
298C2×#388—111no—
299C2×#387—111no—
300C2×#387—111no—
301C2×#386—111no—
302C2×#386—111no—
303C2×#385—111no—
304C23×C11—28no—
305C23×C11—28no—
306C23×C11—28no—
307C23×C11—22no—
308C23×C11—22no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—44no—
314C23×C11—44no—
315C23×C11—44no—
316C23×C11—44no—
317C23×C11C22×D412yes—
318C23×C11C22×D412yes—
319C23×C11C2×#4114yes—
320C23×C11C2×#4112yes—
321C23×C11C2×#4112yes—
322C23×C11C2×#4112yes—
323C23×C11H(5,𝔽2)12yes—
324C23×C112−1+412yes—
325C23×C11C2511yescharacteristic
326C22×D11—28no—
327C22×D11—28no—
328C22×D11—28no—
329C22×D11—28no—
330C22×D11—28no—
331C22×D11—28no—
332C22×D11—22no—
333C22×D11—22no—
334C22×D11—22no—
335C22×D11—22no—
336C22×D11—22no—
337C22×D11—22no—
338C22×D11—22no—
339C22×D11—22no—
340C22×D11—22no—
341C22×D11—22no—
342C22×D11—22no—
343C22×D11—22no—
344C22×D11—44no—
345C22×D11—44no—
346C22×D11—44no—
347C22×D11—44no—
348C22×D11—44no—
349C22×D11—44no—
350C22×D11—44no—
351C22×D11—44no—
352C22×D11C2×#4114yes—
353C22×D11C2×#4114yes—
354Q8×C11—416no—
355C2×C4×C11—28no—
356C2×C4×C11—28no—
357C2×C4×C11—28no—
358C2×C4×C11—28no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—22no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—22no—
373C2×C4×C11—416no—
374C2×C4×C11—44no—
375C2×C4×C11—44no—
376C2×C4×C11C22×D414yes—
377C2×C4×C11C22×D414yes—
378C2×C4×C11C22×D414yes—
379C2×C4×C11C22×D414yes—
380C22⋊D11—232no—
381C22⋊D11—416no—
382C2×Dic11—28no—
383C2×Dic11—28no—
384C2×Dic11—22no—
385C2×Dic11—22no—
386C2×Dic11—22no—
387C2×Dic11—22no—
388C2×Dic11—22no—
389C2×Dic11—22no—
390C2×Dic11—22no—
391C2×Dic11—22no—
392C2×Dic11—22no—
393C2×Dic11—22no—
394C2×Dic11—22no—
395C2×Dic11—22no—
396C2×Dic11—22no—
397C2×Dic11—22no—
398C2×Dic11—22no—
399C2×Dic11—22no—
400C2×Dic11—44no—
401C2×Dic11—44no—
402C2×Dic11—44no—
403C2×Dic11—44no—
404C2×Dic11C22×D414yes—
405C2×Dic11C22×D414yes—
406D44—232no—
407C4×D11—416no—
408C4×D11—416no—
409C23×Q8C2×D1111yescharacteristic
410C23×D4—111no—
411C23×D4—111no—
412C23×D4—111no—
413C24×C4—111no—
414C24×C4—111no—
415C24×C4C2×D1111yescharacteristic
416C2×C22⋊Q8—28no—
417C2×C22⋊Q8—118no—
418C2×C22⋊Q8—228no—
419C2×C22⋊Q8C2×D1118yescomplemented
420C2×C4×D4—118no—
421C2×C4×D4—118no—
422C2×C4×D4—228no—
423C2×C4×D4—228no—
424C22×C4⋊C4—111no—
425C22×C4⋊C4—111no—
426C22×C4⋊C4—111no—
427C22×C4⋊C4C2×D1111yescharacteristic
428C22×C4⋊C4C2×D1111yescharacteristic
429C22×C4⋊C4C2×D1111yescharacteristic
430C22×C22⋊C4—111no—
431C22×C22⋊C4—111no—
432C22×C22⋊C4—111no—
433C22×C22⋊C4—111no—
434C22×C22⋊C4—111no—
435C22×C22⋊C4—111no—
436C22×C22⋊C4—111no—
437C22×C22⋊C4—111no—
438C22×C22⋊C4—111no—
439C22×C22⋊C4—111no—
440C22×C22⋊C4C2×D1111yescharacteristic
441C22×C22⋊C4C2×D1111yescharacteristic
442C22×C42—111no—
443C22×C42—111no—
444#394—118no—
445#394—118no—
446#393—118no—
447#392—118no—
448#388—118no—
449#388—118no—
450#387—118no—
451#387—118no—
452#386—118no—
453#386—118no—
454#385—118no—
455C2×#95—111no—
456C2×#95—111no—
457C2×#95—111no—
458C2×#95—111no—
459C2×#95—111no—
460C2×#95—111no—
461C2×#95—111no—
462C2×#95—111no—
463C22×C11—24no—
464C22×C11—24no—
465C22×C11—24no—
466C22×C11—42no—
467C22×C11—42no—
468C22×C11—42no—
469C22×C11—42no—
470C22×C11—416no—
471C22×C11#52514yes—
472C22×C11#52514yes—
473C22×C11#53914yes—
474C22×C11D4214yes—
475C22×C11#54814yes—
476C22×C11#54814yes—
477C22×C11#55114yes—
478C22×C11C23×D411yescharacteristic
479C22×C11C23×D411yescharacteristic
480C22×C11C22×#4111yescharacteristic
481C22×C11C22×#4111yescharacteristic
482C22×C11C22×#4111yescharacteristic
483C22×C11C2×H(5,𝔽2)11yescharacteristic
484C22×C11C2×2−1+411yescharacteristic
485C2×D11—24no—
486C2×D11—24no—
487C2×D11—24no—
488C2×D11—24no—
489C2×D11—24no—
490C2×D11—24no—
491C2×D11—42no—
492C2×D11—42no—
493C2×D11—42no—
494C2×D11—42no—
495C2×D11—42no—
496C2×D11—42no—
497C2×D11—42no—
498C2×D11—42no—
499C2×D11—416no—
500C2×D11—416no—
501C4×C11—24no—
502C4×C11—24no—
503C4×C11—24no—
504C4×C11—24no—
505C4×C11—42no—
506C4×C11—42no—
507Dic11—24no—
508Dic11—24no—
509Dic11—42no—
510Dic11—42no—
511Dic11—42no—
512Dic11—42no—
513C25—111no—
514C25—111no—
515C25C22×D1111yescharacteristic
516C22×Q8—24no—
517C22×Q8—24no—
518C22×Q8—42no—
519C22×Q8C22×D1114yes—
520C22×D4—114no—
521C22×D4—114no—
522C22×D4—114no—
523C22×D4—224no—
524C22×D4—224no—
525C22×D4—224no—
526C22×D4—224no—
527C22×D4—224no—
528C22×D4—224no—
529C22×D4—224no—
530C22×D4—224no—
531C22×D4—442no—
532C23×C4—24no—
533C23×C4—24no—
534C23×C4—42no—
535C23×C4—111no—
536C23×C4—111no—
537C23×C4—111no—
538C23×C4—111no—
539C23×C4—111no—
540C23×C4—111no—
541C23×C4—114no—
542C23×C4—114no—
543C23×C4—224no—
544C23×C4—224no—
545C23×C4—224no—
546C23×C4—224no—
547C23×C4—442no—
548C23×C4—442no—
549C23×C4C22×D1111yescharacteristic
550C23×C4C22×D1111yescharacteristic
551C23×C4C22×D1114yes—
552C23×C4C22×D1111yescharacteristic
553C23×C4C22×D1111yescharacteristic
554C23×C4C22×D1111yescharacteristic
555C23×C4C22×D1111yescharacteristic
556C22⋊Q8—232no—
557C22⋊Q8—2232no—
558C4×D4—2232no—
559C4×D4—2232no—
560C2×C4⋊C4—24no—
561C2×C4⋊C4—24no—
562C2×C4⋊C4—118no—
563C2×C4⋊C4—114no—
564C2×C4⋊C4—114no—
565C2×C4⋊C4—114no—
566C2×C4⋊C4—224no—
567C2×C4⋊C4—224no—
568C2×C4⋊C4C22⋊D1118yescomplemented
569C2×C4⋊C4C22×D1114yes—
570C2×C4⋊C4C22×D1114yes—
571C2×C4⋊C4C22×D1114yes—
572C2×C22⋊C4—24no—
573C2×C22⋊C4—24no—
574C2×C22⋊C4—114no—
575C2×C22⋊C4—114no—
576C2×C22⋊C4—114no—
577C2×C22⋊C4—114no—
578C2×C22⋊C4—114no—
579C2×C22⋊C4—114no—
580C2×C22⋊C4—114no—
581C2×C22⋊C4—114no—
582C2×C22⋊C4—114no—
583C2×C22⋊C4—114no—
584C2×C22⋊C4—224no—
585C2×C22⋊C4—224no—
586C2×C22⋊C4—224no—
587C2×C22⋊C4—224no—
588C2×C22⋊C4—224no—
589C2×C22⋊C4—224no—
590C2×C22⋊C4—224no—
591C2×C22⋊C4—224no—
592C2×C22⋊C4—224no—
593C2×C22⋊C4—442no—
594C2×C22⋊C4C22×D1114yes—
595C2×C22⋊C4C22×D1114yes—
596C2×C42—114no—
597C2×C42—114no—
598C2×C42—224no—
599C2×C42—224no—
600#95—114no—
601#95—114no—
602#95—114no—
603#95—114no—
604#95—114no—
605#95—114no—
606#95—114no—
607#95—114no—
608C2×C11—44no—
609C2×C11#246318yescomplemented
610C2×C11C2×#52511yescharacteristic
611C2×C11C2×#52511yescharacteristic
612C2×C11C2×#53911yescharacteristic
613C2×C11C2×D4211yescharacteristic
614C2×C11C2×#54811yescharacteristic
615C2×C11C2×#54811yescharacteristic
616C2×C11C2×#55111yescharacteristic
617D11—44no—
618D11—44no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—114no—
626C24—114no—
627C24—112no—
628C24—112no—
629C24—222no—
630C24—222no—
631C24—222no—
632C24—222no—
633C24—222no—
634C24—222no—
635C24—222no—
636C24—222no—
637C24—222no—
638C24—222no—
639C24—222no—
640C24—222no—
641C24#434314yes—
642C24C23×D1112yes—
643C24C23×D1111yescharacteristic
644C2×Q8—28no—
645C2×Q8—28no—
646C2×Q8—44no—
647C2×Q8—416no—
648C2×D4—228no—
649C2×D4—228no—
650C2×D4—2232no—
651C2×D4—228no—
652C2×D4—228no—
653C2×D4—2232no—
654C2×D4—228no—
655C2×D4—228no—
656C2×D4—228no—
657C2×D4—228no—
658C2×D4—444no—
659C2×D4—4416no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—28no—
675C22×C4—28no—
676C22×C4—44no—
677C22×C4—416no—
678C22×C4—114no—
679C22×C4—114no—
680C22×C4—112no—
681C22×C4—112no—
682C22×C4—112no—
683C22×C4—112no—
684C22×C4—112no—
685C22×C4—112no—
686C22×C4—228no—
687C22×C4—228no—
688C22×C4—222no—
689C22×C4—222no—
690C22×C4—222no—
691C22×C4—222no—
692C22×C4—222no—
693C22×C4—222no—
694C22×C4—222no—
695C22×C4—222no—
696C22×C4—222no—
697C22×C4—222no—
698C22×C4—222no—
699C22×C4—222no—
700C22×C4—222no—
701C22×C4—222no—
702C22×C4—222no—
703C22×C4—222no—
704C22×C4—228no—
705C22×C4—228no—
706C22×C4—444no—
707C22×C4—444no—
708C22×C4—4416no—
709C22×C4—4416no—
710C22×C4D4×D1114yes—
711C22×C4C2×C22⋊D1114yes—
712C22×C4C2×C22⋊D1114yes—
713C22×C4C2×C22⋊D1114yes—
714C22×C4C23×D1112yes—
715C22×C4C23×D1112yes—
716C22×C4C23×D1112yes—
717C22×C4C23×D1112yes—
718C22×C4C23×D1112yes—
719C22×C4C23×D1112yes—
720C4⋊C4—28no—
721C4⋊C4—28no—
722C4⋊C4—1116no—
723C4⋊C4—228no—
724C4⋊C4—228no—
725C4⋊C4C2×C22⋊D11116yescomplemented
726C22⋊C4—28no—
727C22⋊C4—28no—
728C22⋊C4—228no—
729C22⋊C4—228no—
730C22⋊C4—228no—
731C22⋊C4—228no—
732C22⋊C4—228no—
733C22⋊C4—228no—
734C22⋊C4—228no—
735C22⋊C4—228no—
736C22⋊C4—228no—
737C22⋊C4—444no—
738C42—228no—
739C42—228no—
740C11C2×#246311yescharacteristic, complemented, Sylow
741C23—28no—
742C23—28no—
743C23—28no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—44no—
751C23—44no—
752C23—44no—
753C23—44no—
754C23—114no—
755C23—114no—
756C23—228no—
757C23—228no—
758C23—228no—
759C23—228no—
760C23—228no—
761C23—228no—
762C23—222no—
763C23—222no—
764C23—222no—
765C23—222no—
766C23—222no—
767C23—222no—
768C23—222no—
769C23—222no—
770C23—222no—
771C23—222no—
772C23—222no—
773C23—222no—
774C23—444no—
775C23—444no—
776C23—444no—
777C23—444no—
778C23—444no—
779C23—444no—
780C23—444no—
781C23—444no—
782C23C2×D4×D1112yes—
783C23#6703712yes—
784C23C2×#434314yes—
785C23C2×#434312yes—
786C23#6704012yes—
787C23#41×D1112yes—
788C23#41×D1112yes—
789C23C22×C22⋊D1112yes—
790C23C24×D1111yescharacteristic
791Q8—416no—
792D4—2232no—
793D4—2232no—
794D4—4416no—
795C2×C4—28no—
796C2×C4—28no—
797C2×C4—28no—
798C2×C4—28no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—416no—
814C2×C4—44no—
815C2×C4—44no—
816C2×C4—114no—
817C2×C4—114no—
818C2×C4—228no—
819C2×C4—228no—
820C2×C4—222no—
821C2×C4—222no—
822C2×C4—222no—
823C2×C4—222no—
824C2×C4—222no—
825C2×C4—222no—
826C2×C4—222no—
827C2×C4—222no—
828C2×C4—222no—
829C2×C4—222no—
830C2×C4—222no—
831C2×C4—222no—
832C2×C4—222no—
833C2×C4—222no—
834C2×C4—222no—
835C2×C4—222no—
836C2×C4—4416no—
837C2×C4—4416no—
838C2×C4—444no—
839C2×C4—444no—
840C2×C4—444no—
841C2×C4—444no—
842C2×C4C2×D4×D1114yes—
843C2×C4C22×C22⋊D1114yes—
844C2×C4C22×C22⋊D1114yes—
845C2×C4C22×C22⋊D1114yes—
846C22—24no—
847C22—24no—
848C22—24no—
849C22—42no—
850C22—42no—
851C22—416no—
852C22—42no—
853C22—42no—
854C22—224no—
855C22—224no—
856C22—224no—
857C22—224no—
858C22—224no—
859C22—224no—
860C22—442no—
861C22—442no—
862C22—442no—
863C22—442no—
864C22—442no—
865C22—4416no—
866C22—4416no—
867C22—442no—
868C22—442no—
869C22—442no—
870C22#1062315814yes—
871C22#1062316414yes—
872C22#1062316814yes—
873C22#1062316914yes—
874C22D4×C22⋊D1114yes—
875C22#1062334814yes—
876C22#1062335914yes—
877C22C22×D4×D1111yescharacteristic
878C22C2×#6703711yescharacteristic
879C22C22×#434311yescharacteristic
880C22C2×#6704011yescharacteristic
881C22C2×#41×D1111yescharacteristic
882C22C2×#41×D1111yescharacteristic
883C22C23×C22⋊D1111yescharacteristic
884C4—24no—
885C4—24no—
886C4—24no—
887C4—24no—
888C4—42no—
889C4—42no—
890C4—224no—
891C4—224no—
892C4—442no—
893C4—442no—
894C4—442no—
895C4—442no—
896C2—44no—
897C2—444no—
898C2—444no—
899C2#1307260918yesdirect product factor
900C2C2×#1062335911yescharacteristic
901C2C2×#1062315811yescharacteristic
902C2C2×#1062316911yescharacteristic
903C2C2×D4×C22⋊D1111yescharacteristic
904C2C2×#1062316411yescharacteristic
905C2C2×#1062334811yescharacteristic
906C2C2×#1062316811yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×C22⋊Q8C2
socleC24×C11C24
prime radicalC2×#10622573C2
hypercenterC22×C22⋊Q8D11
hypocenterC11C2×#2463
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×#66999C2semidirect
2. C22×#66946C2semidirect
3. C22×C4×C22⋊D11C2semidirect
4. #13072609C2direct (N × H)
5. C2×#10622604C2semidirect
6. C2×#10622574C2semidirect
7. C2×#10622844C2semidirect
9. C2×#10622603C2semidirect
10. C2×#10622557C2semidirect
11. C2×#10622594C2semidirect
12. C2×#10622591C2semidirect
13. C2×#10622826C2semidirect
14. C2×#10622569C2semidirect
15. C2×#10622602C2semidirect
16. C22×C11×C22⋊Q8C2semidirect
25. C2×C11×C22⋊Q8C22semidirect
34. C2×#66999C22semidirect
36. C2×C4×C22⋊D11C22semidirect
51. C2×#66946C22semidirect
52. #10622844C22semidirect
53. #10622826C22semidirect
62. #10622604C22semidirect
63. #10622603C22semidirect
64. #10622602C22semidirect
65. #10622594C22semidirect
66. #10622591C22semidirect
67. #10622574C22semidirect
69. #10622569C22semidirect
70. #10622557C22semidirect
117. C2×C11×C4⋊C4D4semidirect
150. C2×Dic11⋊C4D4semidirect
270. C11×C4⋊C4C2×D4semidirect
285. Dic11⋊C4C2×D4semidirect
289. C22×C22⋊Q8D11semidirect
419. C2×C22⋊Q8C2×D11semidirect
568. C2×C4⋊C4C22⋊D11semidirect
609. C2×C11#2463semidirect
725. C4⋊C4C2×C22⋊D11semidirect
740. C11C2×#2463semidirect
899. C2#13072609direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#669992
C22×#669462
C22×C4×C22⋊D112
#130726092
C2×#106226042
C2×#106225742
C2×#106228442
C2×#106225732
C2×#106226032
C2×#106225572
C2×#106225942
C2×#106225912
C2×#106228262
C2×#106225692
C2×#106226022
C22×C11×C22⋊Q82
C2×#246311